Preheat the oven to 180ºC, gas mark 4. Wash the rhubarb, cut into 3cm pieces then place in a pan. Cover and cook gently in the oven for 8-10 minutes until tender. Spoon into a shallow dish and leave to cool.
Beat half the butter (75g) with the caster sugar until pale and light, then beat in the eggs, one at a time. Sift the flour with the baking powder and ground ginger and fold into the creamed ingredients, along with the cooled rhubarb. Spoon into a buttered 1.75 litre shallow baking dish and level the surface. Cook for 30-35 minutes until well-risen and firm to the touch.
While the pudding is cooking, place the cream, muscovado sugar, ginger and remaining butter together in a pan. Heat until melted, then cook gently, stirring occasionally, for 3-4 minutes until thick. Set aside. Remove the pudding from the oven and pour the sauce over it. Return the dish to the oven for 5 minutes until bubbling and golden. Serve with vanilla ice cream.